The Fekete and Szegő Problem for a Class of Holomorphic Mappings Associated with Starlike Mappings on the Unit Balls of Complex Banach Spaces

In this paper, we first establish a refinement of the coefficient inequality for subordinate functions on the unit disc \(\mathbb{U}\) $$\mathbb{U}$$ in \(\mathbb{C}\) $$ℂ$$ . Next, as applications of this inequality, we will obtain some refinements of the Fekete and Szegő inequalities for a class of holomorphic mappings associated with starlike mappings and quasi-convex mappings of type B on the unit ball \(\mathbb{B}\) $$\mathbb{B}$$ of a complex Banach space. The results presented here would generalize and improve some recent works of several authors [12, 20, 23].